Thank you, Messrs. Rich, Boss, Miller and McCormick
for the helpful replies.
I can add to the list of solutions the following:
diffadv=: 1 :'(}. - }:)^:u'
2 diffadv (i.10)^5
30 180 570 1320 2550 4380 6930 10320
Although I don't know how to refer to them, I find two
very different contexts in J composition. One is where
verbs are *used*, the other is where verbs are
*formed.* Examples of each, here:
list=: (i.10)^5
order=: 3 NB. i.e. third-order
]noun=: (}. - }:)^:order list
150 390 750 1230 1830 2550 3390
]verb=: (}. - }:)@]^:[
] (}. - }:)@]^:[
order verb list
150 390 750 1230 1830 2550 3390
I do not yet properly grasp why the two nouns that
come into play must be reorganized between these two
modes. To demonstrate that they must, this is what
happens when we try to use the verb-forming
construction for immediate calculation:
]noun=: (}. - }:)@list^:order
|domain error
| ]noun=: (}.-}:)@list^:order
Not that this would look right to me in the absence of
an error message, for the diff function (}. - }:)
needs to be processing distinct data on each pass, and
this seems to specify that the same data should be
bound each time.
My guess, interpreting the verb-making form, is that ]
denotes values that differ on each cycle. If this is
accurate, I've learned something about power.
What still eludes me, though, is a naturalness in
reading, such that I anticipate this reversal of
power-specification and data when moving from full
calculation to tacit definition.
At this point, however, I have several engaging
variations in hand for study. Thanks, again.
Tracy
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